Tomatoes with dark, sunken blemishes on the blossom end (opposite to the stem end) are suffering from blossom end rot. This is not a disease but a condition caused by stress to the plant at a time when it is setting fruit. Calcium is critical to the proper formation of the tomato. When the plant gets stressed (typically, when a plant has insufficient water and wilts on hot days at a time when the plant is doing a lot—growing vigorously, blossoming, and setting fruit), calcium availability in the developing tomatoes is insufficient, leading to the end rot. Occasionally, the pH of the soil in which the plant is growing is too acidic, which prevents adequate calcium uptake.
To minimize blossom end rot, ensure the pH of the soil is between 6 and 6.8; if lower than 6, add the calcium source of your choice. Be sure that your plants don’t wilt during the hottest part of the day, particularly if the plant has lots of small green fruit, by ensuring adequate water. Use of drip irrigation or self-watering containers is very effective.
Even if you follow all of these suggestions, you may find blossom end rot on the first tomato or two from a plant; future tomatoes are typically fine. Some varieties are particularly prone to blossom end rot, such as sauce (plum or paste) tomatoes, due to their very heavy fruit set.