The answers to the clues on the left (in alphabetical order as a solving aid) are often reduced to a three-letter abbreviation (for Twitter, text messages, scoreboards, etc.):

• Be right back = BRB
• Chicago White Sox = CWS
• Downloadable content = DLC
• Guns N' Roses = GNR
• Home Shopping Network = HSN
• Mainstream media = MSM
• Neil Patrick Harris = NPH
• New South Wales = NSW
• No big deal = NBD
• Salt Lake City = SLC
• Scott van Pelt = SVP
• Social Security number = SSN
• The Next Generation = TNG
• To be honest = TBH

The answers to the clues on the right all contain exactly three consonants, matching a set from the left:

• season = SSN
• save up = SVP
• ECOWAS = CWS
• ignore = GNR
• sluice = SLC
• Hosni = HSN
• in bed = NBD
• Barbeau = BRB
• museum = MSM
• Tobiah = TBH
• unsew = NSW
• Dolce = DLC
• anaphia = NPH
• teenage = TNG

Each line connecting a pair crosses exactly one numbered circle:

The number indicates which letter to take from the TLA. In order by the right column, these spell NSWRSNDRSTNDNG. Place a few vowels to get "answer is UNDERSTANDING".