This idiom or expression like phrase (in sports) means:

Not enough challenge.

When someone says “Did you see the match last night? It was no contest,” they mean:
It wasn’t a fair match.
The two sides were not fairly matched.
One side was very clearly superior to the other. Etc.

This idiom or expression like phrase (in legal context) means:

No challenge.
No argument.

When someone says “She pleaded no contest to the charges,” they mean:
She offered no argument.
She didn’t challenge the charges.
She didn’t admit that she was guilty, but she also didn’t say she was innocent.