"Representation" is a broad term encompassing all manner of tasks that a lawyer can perform for a client, including providing advice, negotiating a deal on a client's behalf, drafting documents, appearing in court, and so on.
Typically, though, a lawyer's representation of a client is limited. A lawyer may agree to provide advice but not to litigate. A lawyer may agree to litigate a case through trial, but not to litigate the appeal. A lawyer may agree to provide advice on a transaction, but not with respect to its tax implications. The exact scope of the representation will usually be made explicit in an engagement agreement between the lawyer and client.
When a lawyer agrees to represent someone in a court case, the client can generally expect her to conduct a factual investigation into the merits of your case, to contact and attempt to negotiate with the opposing party, to draft and file any paperwork necessary to litigate the case, and to appear and argue in court on the client's behalf.
A client is typically not obligated to follow his lawyer's instructions. Instead, the reverse is typically true, at least with respect to major decisions. When it comes to tactical questions and the day-to-day prosecution of the case, a lawyer typically has broad discretion to handle the case as she sees fit, so the client shouldn't expect to have the opportunity to revise her e-mails or otherwise micromanage the lawyer. A client like that should expect to be fired, unless he is paying very handsomely.
The lawyer has a duty to appear in court on your behalf and handle other time-sensitive matters. A lawyer who cannot meet those obligations will typically request that the court extend the time available for a filing or reschedule a hearing to a date when she will be available. Courts are typically very willing to do so. If a lawyer fails to do these things, she may be liable to the client for malpractice.