What happens if my circumstances change - for example, if I am widowed, and then get married again?

If you are widowed, your current will remains valid but any gift that would have gone to your spouse lapses. This can dramatically change the effect of your will: for example, if your will left most of what you own to your spouse. Your best course is to draw up a new will.
Any subsequent marriage (or entry into a civil partnership) will completely invalidate your current will, unless that will was drawn up in the expectation of the marriage and mentions it. Unless this is the case, you need to draw up another will, preferably before the ceremony.
The same applies to any major changes in circumstances. If your will might no longer reflect your wishes, you need to update it.