To bite off more than you can chew means to take on a very big task that you cannot manage. This is akin to the situation when you bite off a piece of pizza, for example, that is much too large - you will find it difficult to chew the entire piece at one go and would likely have to remove a bit of it from your mouth.
1. The ISC Editor willingly took up the task given to her by the Webmaster but within a day realized that she had bit off more than she could chew as there was a huge backlog of editing work too.
2. The young architect enthusiastically agreed to design the bungalow but lack of experience made him realize that he was biting more than what he could chew.
3. When the group of small firms got together to host the International seminar, they had bitten off more than they could chew as they just did not have enough funds.