Directory permissions - write. What and How to change?

[landyvlad]

I am getting errors trying to upload and install packages

You cannot download or install new packages because the Packages directory, or one of the files in it, is not writeable!

An error has occurred
Unable to upload package. Please check directory permissions!

Now this only appears to have occurred since I changed the hosting company so I presume (but may be wrong) that there were permission changes which occurred due to that?

What I need to know please - for the packages directory specifically but also for the forum generally is:
Which directories need write permission and is there an ideal permissions code (ie the 3 digit number) to use for those directories?

Ta.

[Illori]

create a folder in the Packages folder named temp.

https://wiki.simplemachines.org/smf/Chmod

[landyvlad]

Well, that worked! Thank you so much

Next Q - WHY did it work (simple english and if its not an easy answer don't worry I don't want you to waste too much time on me. 

[Kindred]

The php system user did not have permission to create the directory

[dodos26]

I once had a problem that it required permissions of the user on which the process was running, and packages were downloaded and saved but for the other user from apache ;P