The two primary issues with cheap built in sound cards is noise level and latency.
Noise in the recording path matters for recording audio – e.g. vocals or real instruments. If they are recorded with added noise, this will affect the quality of the recording. Note, that many techniques of processing music amplify the signal and thus the noise – e.g. compression or distortion effects, commonly used for electric guitars.
With 16 bit resolution the noise level can't be lower than -96dB. In practice, the input noise is often much higher, due to poor quality analog path. 24 bits allow for noise of -144 dB, in practice good interfaces are better than -110 dB noise.
As the others point out, line input is not suitable for connecting passive guitar due to impedance mismatch, and may result in loosing high frequencies from the signal.
The latency matters for live audio processing in the PC, that is playing virtual instruments using a MIDI controller (e.g. MIDI keyboard), or using effects – such as your Guitar Rig. With big latency, there will be perceivable time delay between playing the note and hearing it back, which may make recording impossible. Some workarounds are possible, but not necessarily convenient.
In what way I will get better sound quality and fidelity by using an Audio Interface at 16bit 44Khz?
First of all, I think nowadays all decent audio interfaces are 24 bit. Good quality 16bit would be still better than poor quality 16bit, due to quality of the analog path and the analog to digital converters (ADC).
The sampling frequency matters less. 44.1 kHz is a compact disc standard, 48 kHz is the most common in consumer digital to analog converters (DAC). In practice, a single conversion of the sampling frequency won't harm the sound quality much.
Higher sampling frequency are most likely waste of the disk space and CPU, unless you're making music for cats. While some processing effects may benefit from oversampling, as it helps to avoid aliasing artifacts, recording at higher frequencies means recording sounds that are inaudible for most humans anyway, and will likely be removed from the final recording anyway.