Modal particles are words that don't have just one clear-cut and specific dictionary definition. But they play a very important part in the meaning of a sentence. They're predominantly used in spoken language (discourse or dialog particles). They convey additional meaning and signalize the speaker's point of view of what is being said. Some of the most common modal particles are "doch" and "mal".

Examples:
Beeilen Sie sich doch!
Beeilen Sie sich mal!

The meaning of modal particles in a sentence depends very much on the context. "doch" can be used, for example, to express frustration or impatience in an imperative. But depending on the emphasis, it can also make a command more indirect, mild and polite. Such imperatives often include the word "bitte".

Examples:
Kommen Sie doch bitte! (polite)
Sei doch mal still! Mein Gott, Harry! (frustration)
Beeilen Sie sich doch! (impatience)
Frag doch mal nach dem Orakel! (suggestion)

Some modal particles can be combined with others.

Examples:
Seien Sie doch mal still!
Kommen Sie doch mal!