Meaning

• (of an object) To join (to another object): to attach, or to be intended to attach or capable of attaching, to another object.

  "I think this piece connects to that piece over there."

• (of two objects) To join: to attach, or to be intended to attach or capable of attaching, to each other.

  "Both roads have the same name, but they don't connect: they're on opposite sides of the river, and there's no bridge there."

• (of an object) To join (two other objects), or to join (one object) to (another object): to be a link between two objects, thereby attaching them to each other.

  "The new railroad will connect the northern part of the state to the southern part."

• (of a person) To join (two other objects), or to join (one object) to (another object): to take one object and attach it to another.

  "I connected the printer to the computer, but I couldn't get it work."

• To join an electrical or telephone line to a circuit or network.

  "When the technician connects my house, I'll be able to access the internet."

• To associate; to establish a relation between.

  "I didn't connect my lost jewelry with the news of an area cat burglar until the police contacted me."

• To make a travel connection; to switch from one means of transport to another as part of the same trip.

  "I'm flying to London where I connect with a flight heading to Hungary."

Meaning

• (usually with "well-"): Having favorable rapport with a powerful entity.

• Having relationships; involved with others.

• Involved with organized crime, specifically someone not (yet) working for a crime organization, but referred to as a "friend" by made guys/wise guys inside the organization.

• Intimate; Having bonds of affection.

• (of a topological space) That cannot be partitioned into two nonempty open sets.

• (of a graph) Having a path, either directed or undirected, connecting every pair of vertices.

  "In a connected graph, there is no section (proper subset that includes all edges from each vertex in said subset) of the graph that is isolated from the rest."

• Having or supporting connections, especially when through technology such as networking software or a transportation network.