GPL
Other developers can borrow and modify the code and re-distribute it as part of their own project, only if their entire project is also licensed under the GPL.
This prevents the code from being used in proprietary software.
LGPL
Other developers can borrow and modify the code and re-distribute it as part of their own project, provided that the portion used under the LGPL, including any modifications, is re-licensed under the LGPL. Other portions of the project are permitted have other licenses.
This allows the code to be used in otherwise proprietary software.
One thing to note is that the LGPL is a longer and more complicated license than the GPL itself, because it contains the full text of the GPL and then adds additional terms to it.
Many of the additional terms in the LGPL specify the conditions that need to be met in order to be able to distribute your code in a project with another license. For example, not only must the user be given the source code to the section under LGPL, but it must be possible for the user of the finished software to modify, re-compile or replace the portion of the software that is licensed under the LGPL and use this modified code with the same software. If you are publishing otherwise proprietary software containing some LGPL code, one way of satisfying this requirement is to place the LGPL code into a separate dynamically linked library, and to distribute with your software the necessary header files and documentation required to re-compile the LGPL portion in such a way that it can still be linked and used with the software as provided. It is not acceptable to take steps to prevent modification of the LGPL code such as obfuscating the code itself or the API or header files.
Note that the LGPL is compatible with the GPL: you can opt to "upgrade" the code to GPL and incorporate it in a wholly GPL licensed project as set out in my first bullet point if you wish. You can't however go the other way and re-license GPL licensed code as LGPL.