I don't see how the "Imagine you are walking" stuff explains time signatures in any way. It only seems to be describing how you can have different rhythms within a 4/4 bar. You cannot always determine exactly what the time signature is from the notes. Two minims in a bar could be 2/2 or 4/4.
The time signature itself tells you how a bar is constructed; the number on top tells you how many beats there are in a bar, and the number below tells you how long those beats are. So 4/4, which is probably the most common signature, means you have four crotchet beats in a bar, and 4/8 means four quaver beats in a bar, and the only difference is in the way the notes are written out - in 4/8 one beat would be one quaver; 8 equal notes in a bar would be 8 semiquavers.
The lower number can be any power of two: 1 for whole note/semibreve, 2 for minims, 4 for crotchets, 8 for quavers etc. Mostly you will only see 2, 4 and 8 here.
The upper number tells you how many beats in a bar unless it's a multiple of 3 (except 3 itself). If it's a multiple of 3 then this indicates compound time; listen to the song "Didn't we have a lovely time the day we went to Bangor"; this has two beats to the bar, but each beat is split into 3. Without compound time this would have to be written in 2/4 but with triplet signs all over the place, so writing it in 6/8 instead makes for cleaner music.
You can have a lot of fun with different numbers on the top. Listen to Take Five; that is in 5/4 time.
Blue Rondo A La Turk is another good one with an odd signature. It's in 9/8, but has two different groupings of notes: 2/2/2/3 and 3/3/3.
7/8 is a very interesting signature; it's one quaver short of the very common 4/4 time, and music in 7/8 can seem somehow incomplete.
Going back to 3's: the signature 3/4 often denotes a waltz, although there is non-waltz music in 3/4 (like the British National Anthem. We've abolished the death penalty for everything except trying to waltz that). Some music will be in 3/8 to indicate clearly this is not to be done as a waltz.
4/4 is also known as common time and can be denoted with a C where the time signature would normally appear. Watch out for "cut common", which is a C with a vertical line through it; this has two beats to the bar but is written out as if in 4/4.