To bite off more than you can chew is to take on a task, commitment, or project that exceeds your capacity. You have made a commitment you cannot comfortably meet. A new employee who volunteers for six simultaneous projects in their first month has bitten off more than they can chew. A small business that accepts too many large contracts at once has bitten off more than it can chew.
The phrase is most plausibly American in origin, arising in the 19th century when chewing tobacco was commonplace across all social classes in the United States. Plugs of chewing tobacco were sold in solid blocks from which users would bite off their portion. Biting off too large a piece was genuinely uncomfortable — you had more than your mouth could manage. The physical experience was immediate and familiar to millions of Americans.
The phrase appears in American print from the 1870s. Some researchers cite a letter attributed to John Adams in 1783 as containing an early version, though the exact wording differs from the modern form. By the late 19th century the phrase was established across the American English-speaking world. It has since spread to all English varieties as chewing tobacco culture declined but the metaphor remained perfectly legible.
No — it applies to any situation where someone has taken on more than they can manage: a diet too extreme to maintain, a financial investment too large for their means, or a social commitment they lack the energy to fulfil.
'Playing it safe,' 'staying within your limits,' or 'not overcommitting' are the corresponding cautious approaches. The idiom 'know your limits' conveys the same caution in the other direction.