Subjunctive

The subjunctive form (base form) is used in noun clauses following verbs or adjectives of urgency, necessity, and advice.

Because I've now introduced the term "noun clauses", here is a quick definition: Noun clauses are dependent clauses that function the same as regular nouns -- they can be subjects, objects, or objects of preposition.
Example: What I want to eat is some tasty catfish.
(Here, "What I want to eat" is the noun clause, coming before the main verb in the sentence.)

Back to the subjunctive.

Here is a list of common verbs and adjectives of urgency, necessity, and advice:
ask*
demand
insist
it is advisable that
it is essential that
it is crucial that
it is important that
it is required that
order*
prefer*
suggest
require*

*These verbs often take the subjunctive, but can also occur is the following pattern:

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VERB + OBJECT + INFINITIVE

Compare:
She asked that we drive her to work. (noun clause)
She asked us to drive her to work. (verb + object + infinitive)

She ordered that she obey the law. (noun clause)
She ordered her to obey the law. (verb + object + infinitive)

Do not forget:
The subjunctive (base form) is used regardless of tense.
For example:
I suggested that she buy the black dress. (My suggestion occurred in the past)

When using the subjunctive, it is impossible to know whether the action in the noun clause will ever happen.
For example:
It's important that he understand. (I don't know if he ever will understand.)