In general as a new user, it is much less hassle to just select "No", when presented with the question Do you want to install from sources the package which needs compilation? (Yes/no/cancel)
in R.
Explanation of the question by R and responses
The question Do you want to install from sources the package which needs compilation? (Yes/no/cancel)
is telling you that one (or more) of the packages you are trying to install has a newer version than what is available as a binary. To understand what this means, you need to understand a bit about the R package ecosystem.
CRAN
The default location where packages are installed from is called CRAN (Comprehensive R Archive Network). This is a web-server (actually many servers world-wide), that has a copy of many R packages. When packages are written for R, they are initially written and submitted to CRAN as source code. The source code submitted to CRAN is then compiled into binary packages for the Windows and Mac OS operating systems.
You could think of it like a clothing shop. You can go to the shop and get a jacket for cold weather, or a hat for sunny weather, or lots of other options.
Binary Packages
Packages are compiled into binaries because they have several advantages: they enable faster installation by end users as the user doesn't need to compile the source code for themselves, which saves them time. They are also easier for users to manage as a user doesn't require extra software or tools, and they tend to be more stable. The downsides however are that the binaries are specific to a particular system, usually an Operating system, and sometimes even particular versions of an operating system. Compiling a package from source takes time, especially if it's a large package. Binaries also (potentially) don't contain the latest version of the code, so there may be bugs that haven't been fixed, or it may be missing new features or additions.
The CRAN Process
When CRAN receives an updated package, it can take a few days to get around to compiling the source code into a binary. In the meantime, if users try to install that package, the message you observed is displayed, giving the user the choice of installing the binary, which is usually much quicker, but may not have some new features or may contain bugs that haven't yet been fixed, or the source code version which is the latest version, but requires the extra tools you discovered.
In the context of a store analogy, you could think of this as new stock for the clothing shop. They have received the new stock, but haven't yet put it out on the racks. You can come back in a few days, or you can find the box (which will need a tool like a knife to open) and unpack it yourself, and then get the item.
Installing from source
As mentioned in the comment by @Bruno, you will need to install Xcode to install packages from source on MacOS or rtools on Windows. Most of the time installing these additional tools is all that's required to build packages from source, but sometimes things may not work so smoothly, which is why installing binaries is usually better.
Aditional note about conflicts
The note you received about conflicts is entirely normal when loading the tidyverse. It's there to alert you to the fact that there are multiple functions with the same name that come from different packages, and this may cause problems if you don't realise. In most cases you don't need to worry about it, but is pretty easy to solve if there are issues.