The posted answers are either behind a paywall or very obtuse so I'll just explain. I'll assume you know what tokens are.

A models output is not a single token, but a list with the probability for all the tokens that it knows, so we need to use a sampler to select the token that it's going to be the next token in the sentence. For example a simple greedy sampler will choose the token with the highest probability, but samplers normally pick a random token weighted by probability. A model usually knows about ~250 thousand tokens and the probability of some of these tokens are gonna be high, but the vast majority is close to but not actually 0% so there's a chance the sampler might pick some random token that doesn't make much sense, so we filter tokens.

top_k filters the tokens so that only the k top tokens are selected. So top_k=50 will filter those 250k tokens to only 50. This is assuming the list of tokens is sorted by probability.

top_p filters the top tokens until a percentage is accumulated. So if for example if you set the top_p to 0.6 and the model gave the top token a 0.5 (50%) probability and the second top token a 0.2, those 2 token accumulated to 0.7 which is greater than what you set it to (0.6) so no more tokens are selected. If this ran after top_k=50 it'll turn the list of 50 tokens into one of 2.

After each filter parameter is processed, the probability of the tokens is adjusted to sum to 1 (100%), Also note that order of operation here matters, i.e. top_p could be applied before top_k, but most providers follow what's on huggingface, I think I've only seen different implementation in certain local model hosting frameworks.