When someone says 'I'll take these odds' I usually take it to mean something like 'I am confident I can overcome this challenge'.
To be sure I went to ask google to see exactly how phrases with the word 'odds' are used and I couldn't find anything resembling my understanding.
For example lexico says the following for the phrase 'take the odds':
Offer a bet with odds unfavourable to the other better.
This contrasts with the phrase 'lay the odds':
Offer a bet with odds favourable to the other better.
This is where it gets confusing for me, these are obviously some betting terms and I wonder if they can be used in the same sense as the understanding I stated above. How can one 'offer' a bet when he is 'taking' a bet? What does 'favourable' mean and who is the 'other better'?