Duston's answer is correct, but I wanted to add a supplementary answer for the context of the OP's question, which contained an example of a rapper referring to the "bars" of a hip hop instrumental. A bar is a term that is easy to define, but the explanation of its usefulness and uses to music as a whole can get a bit abstract and/or lead to more questions (what is a time signature? Are bars only useful for sheet music? etc). But in the context of a hip hop instrumental, it's fairly simple to describe what a bar is and why it is useful, because the instrumental is usually just a looped phrase, with all the focus being on the lyrical content and delivery.
Bars, as Duston explained, is a "measure". In 4/4 music, there are 4 beats within a measure or bar.
Speaking in general terms of a regular hip hop instrumental (often referred to as a "hip hop beat", but I don't want to get that confused with the concept of a "beat" being the time kept within the music), the majority of hip hop instrumentals are in 4/4 time, so most of the time you'll hear four beats along the lines of "boom (bass), bap (snare), boom (bass), bap (snare)", constituting one bar. An instrumental will generally keep the snare on beat 2 and 4 all the time, so if you can count the snares, you can count the bars (two snare hits per bar). If you pull up nearly any hip hop song, you can probably count each beat with "1, 2, 3, 4...1, 2, 3, 4", with the snare being the 2 and 4.
Because rappers generally want to rap with the beat, it's important to know what the instrumental is doing, and understanding the concept of bars and beats helps orient a rapper within the instrumental. For a basic instrumental beat loop, where the same "notes" repeat for every single bar, all that a rapper needs to do is understand four beats, which is pretty easy to keep track of. For example, the instrumental for Mobb Deep's "Shook Ones Pt. II", which was famously used as the beat for the final freestyle in 8 Mile, repeats the same snare/bass rhythm for every bar (you can count the two snare hits, and then know that the music will loop back around and repeat what you just heard). This simple looping makes an instrumental more suitable for freestyling, because the rapper doesn't need to focus too much on what the beat is doing; it's just the same four beats over and over.
However, it's common for hip hop instrumentals to have two bar loops, or even four bar loops. For example, if you listen to Outkast's B.O.B. song, the instrumental is a two bar "phrase" (collection of bars) that repeats itself - at least in the portions with the vocals. The first bar of the phrase (the part containing the first two snare hits) is a bit sparse with the bass which leaves the music feeling kind of empty, but the second bar (the part containing the next two snare hits) has several bass hits going on, making the second bar sound a lot busier.
The most important benefit that a rapper can gain by understanding when a bar or multi-bar phrase starts or ends is, obviously, knowing when to start and stop rapping. It usually sounds odd if a rapper begins rapping in the middle of a bar, or stops rapping before a bar or phrase ends. The concept of bars and phrases also helps a rapper understand when to pause for a breath or change lyrical subjects. But at a more skilled level, it also lets the rapper craft their lyrical performance around the instrumental. As a very simple example from the B.O.B. song, we hear Andre 3000 spew out "but this'll be the year that we won't forget" in a single bar, very quickly and jumbly during the second bar of the phrase, where the bass is also quick and busy and jumbly; but then the very next line simply says "one nine, nine nine", stretched out across the entire bar at the beginning of the next phrase, where the bass is spaced out and empty. The delivery of the two lines are very different (one fast and jumbly, the other long and drawn out), but they work well with the underlying instrumental.
For many people, this all comes instinctually. But this little bit of music theory is a very useful tool for visualizing an instrumental, and orienting yourself within it. This is the definition of "bars" that 50 Cent was referring to, and it's generally what "bars" means to most musicians.
For completeness, and to address the second quote in OP's question from B Reath (which uses "bars" in a different context than the 50 Cent quote), I should also mention that the term "bars" is a slang term in the hip hop world, with a few different meanings. Generally when a rapper brags that they've "got bars", or their "bars are fire", or they can "go bar for bar against any rapper", they're actually referring to lyrics that are rapped over bars of instrumental music. In that context, the lyrics are implied to be very good, or at least have substance. Somebody is likely to listen to Eminem's "Lose Yourself" and exclaim that Eminem has "got bars", but they would be unlikely to say that after listening to "Gucci Gang".
Other times, rappers will refer to a number of bars, which represents how many bars they have been/are rapping over. Kind of like how an author uses a word count for their own metrics. Most rap verses last for 8, 16, or 32 bars (note that the bar counts are generally multiples of 2 or 4, since a looping phrase could consist of 1, 2, or 4 bars), so it's not uncommon for a rapper to have a line like "that was 32 bars, here's another 32 more" to emphasize that they're rapping for an extended period. But more importantly, for the rapper themselves, knowing what bar they're on in the instrumental will help them understand where they are in the instrumental overall. This is useful for both freestyling, and for writing or recording written lyrics - if you've got a lyrical theme running through the verse, you'll probably want to structure it around a beginning, middle, and end.
Ultimately, bars are just the containers for a collection of notes for a specific number of beats. But they're building blocks that help build the foundation for how a person writes, performs, and understands music.