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Normally, once the active and passive articulators have cut off the airflow by touching, they have to move apart again and let the airflow resume.
Many languages require their stops to be released. English doesn't. It's possible to release the final stop in an utterance, e.g., That's my cat, but it's not necessary. Because it's usually not necessary, it usually doesn't happen.
IPA marks an unreleased stop (or a stop whose release can't be heard) with the "corner" diacritic: [kæt ̚].
The absence of a release is even more obvious in a compound word like catnip. Here, the tongue tip touches the alveolar ridge at the beginning of the [t] and stays there all the way through to the end of the [n]: [kæt ̚nɪp].
The same situation occurs in words like button [ˈbʌt ̚n̩] and widen [ˈwajd ̚n̩]. In normal speech, there is no vowel in the second syllable of these words -- the airflow remains blocked at the alveolar ridge throughout the entire syllable.
In situations like this, it is often (unfortunately) said that the stop is nasally released, which you can transcribe with a superscript [ⁿ] if you're desperate, as in [ˈbʌtⁿn̩]. There are also lateral releases: in a word like bottle, the tongue tip doesn't completely leave the alveolar ridge after the [t], only the sides of the tongue drop down to form the following [l]. This kind of release can be transcribed with a superscript [ˡ], as in [ˈbɑtˡl̩].
Finally, the unreleased diacritic [ ̚] can also be used for situations like [ˈdɑk ̚tɹ̩], when the release of one stop happens during the medial phase of another stop, as discussed in the page on overlapping segments. (You might also see the tie sign used to join the overlapping segments, as in [ˈdɑk͡tɹ].)