This is quite clear from name that what is manual and automation testing? One is done manually through human efforts while other one is carried out by the automation tools that run with the help of scripts.
Manual testing: this type of testing is totally based on human intervention where test case are prepared and run totally by human efforts. This method requires well trained professional so overall cost can go high for this type of project. Any type of application can be tested manually but there are some limitations too. If project is of very large scale then manual testing takes lot of time. Some parts of testing like load testing and stress testing can’t be done manually. This process often becomes repetitive because same work is done again and again.
Automation testing: various automation tools are used to run testing campaign. If you have big project and work on regular basis then these tools can save your plenty of time and money. This is very useful for the regression style of testing. Tools can run same script as many times as you need. Some prominent testing tools are Selenium, QTP, Jmeter, LoadRunner, Test Link etc.
If you want more information about various ways of software testing then we have many more blogs that you can read.