Abarim Publications' online Biblical Hebrew Dictionary
The Aramaic word בר (bar) is cognate of the Hebrew word בן (ben), basically meaning son, much like the son-part in the English name Johnson, or the Mac-part in the name MacDonald (see the article on the word בן (ben) under the name Ben). This Aramaic word is used sporadically in the Hebrew Bible (Proverbs 31:2, Psalm 2:12). Why the Aramaic language uses the letter ר (resh) while most Semitic languages use the ן (nun) is a mystery, but a similar ר (resh) and נ (nun) swap occurs in the name Nebuchadnezzar/Nebuchadrezzar.
Note that the Aramaic noun בר (bar) is identical to one Hebrew adjective meaning pure or clean, and one Hebrew noun denoting a kernel of grain (which in Biblical Aramaic occurs with the meaning of field - Daniel 2:38, 4:9). These words derive from the verb ברר (barar), meaning to clean or purify.
In compounds, such as names, the word bar may also denote a smaller version of something, or someone sharing a characteristic with someone, or someone who's acquired a certain skill or characteristic.