When an offense is faced with a 3rd down, execution becomes more crucial. 3rd down conversions are often used to determine the best offenses, but this can be misleading; the best offenses will have lower numbers of 3rd downs overall because they will have already reached the line to gain on either 1st or 2nd down.
Depending on the amount of yards a team needs to get a first down, offenses will run either a pass or run play for the 1st down. When it is 3rd down and the offense needs more than three yards, they will almost always be running a passing play, because a run can be too risky. Alternatively, coaches will usually choose to run the ball on 3rd and short situations, although passing in short yardage scenarios is becoming more popular in the NFL as offenses try to trick defenses.
Of course, defensive backs are alternatively taught to "play the sticks" on 3rd down so that they may prevent receivers from reaching the line to gain.
3rd downs are often the most important down for both offenses and defenses because they both have the most to gain and lose. Failing to convert a 3rd down means an offense will face 4th down, and likely be forced to punt the ball back to their opponent or settle for a field goal attempt. Additionally, defenses hate giving up 3rd down conversions because they have almost completely stalled an offense's drive, but fell short at the last moment.