What is the meaning of "need access to: " in when we want to install an application? Whenever we want to install an application from Google Play, the application will ask permission to access to some things. The number of permissions are different from one to another application. Below is an example of application that requests permission to access.

Then my question are, how that access work? Is the application will take our data for them? I.e: It ask to access images in the phone, will the application will copy and send all the images to the developer? Or, will the application copy the conversation as it has access to the microphone? And how long it will have the access one we granted and installed the application?
Is the application will take our data for them? I.e: It ask to access images in the phone, will the application will copy and send all the images to the developer? Or, will the application copy the conversation as it has access to the microphone? 


There is no authoritative answer to this in the absence of the source code of the software being available for review, and of course, one's ability to review the code themselves. The applications are written by actors, developer(s) technically. That actor may be benign and genuine and minding just their business, literally and figuratively, so they would mention it in their terms of use policy that to what extent and what category of data would be collected. 

However, a malicious actor would naturally want to have access to all the private data of yours, so their app may listen to your private conversations, use your camera, upload your photos and so on once you have granted access to the permissions it would have demanded. 

Some detection and preventive safeguards can be deployed, but that matter is beyond the scope of this question here. 


  And how long it will have the access one we granted and installed the application?


Since Marshmallow, a user can revoke or grant certain dangerous permissions later in time even if they had been granted earlier, by going into Settings > Apps. The permissions stay as long as the app stays in the device. Once you uninstall an app, all granted accesses are lost, but not the data that it may have collected and uploaded somewhere else. A reinstallation is no different than a fresh installation in terms of permissions access.