If you're on a PC then Camtasia is great. - but paid for.
There are other solutions for Mac

I just use Jing. It's free. It has their branding in the corner and is hosted by them, but I don't care about that. If the screencast works and it gets the job done, our customers don't care (and have yet to complain)

It depends. Are these screencasts you are wanting to record? On the Mac, I use Quicktime these days as it is included and seems to be more stable than other solutions. You can also record using the camera on your laptop. I am not sure if you can use Quicktime to record both your screen and your camera at the same time. If you are on a PC, I believe Microsoft Expression Encoder 4 can do this.

Modern Operating Systems have built-in support for screen recording.

Windows: http://winsupersite.com/windows-10/how-use-windows-10s-screen-recording-utility
Mac: https://support.apple.com/en-us/HT201066

There are also more powerful standalone applications like Camtasia that are popular, but all allow you to record your screen and an audio source like your computer's microphone.

Hope this helps.