We can best explain what logistic regression does by an example problem:
Example:
Assume that we are
As can be seen, logistic regression is a binary classification problem. It is quite different from the usual linear regression.
In linear regression, we try to find a relation of the form
\begin{eqnarray}
y=\beta_0+\beta_1 x
\end{eqnarray}
between dependent and independent variables. In logistic regression, we try to find a relation like
\begin{eqnarray}
p = f(x)
\end{eqnarray}
which gives the probability of $p$ of $x$ belonging to class 1.