An interesting aspect of music is that a time signature is merely a framework to help describe the actual music and that with syncopation and other variations, what is written in 4/4, for example, can sound like a different time signature. What is important to understand is that music is something beyond what is traditionally taught and understood.
Filling up a chart by the lines on the paper is like painting by the numbers. Sure, you can make a very nice painting by following the numbers and using the techniques developed over the years, but if you want to be your own fish, you have to jump out of school.
The human ear needs time to get used to sounds it is unfamiliar with, but once it does, those new sounds can offer extra dimensions to musical expression. Always be open to sounds that don't appeal to you at first. Given time, even the harshest and oddest sounds can turn pleasurable. This appreciation will then give you a greater choice of musical entertainment and expression.
RE: Time Signatures in music - why do they matter? What is 4/4 anyway? [my answers]