Except Access

You're allowed enter the street (or make a left turn, or whatever) if your destination is somewhere on that actual street, so the only way you can get to it is by entering that street. You need to access somewhere on that street.

In contrast, if you would be just passing along the street on your way to somewhere else (not accessing somewhere on the street itself) then you could potentially take other routes to where you need to go. You don't need to use this particular street. So you're not allowed enter it because it's not required for getting to your destination. You don't need access.

There may be an entire zone of streets that are 'no entry except access', especially if there are roads that are one-way or one lane but two-way. There are other restrictions that may be 'except access', for example limiting the weight of the vehicle is very common. In that case, heavier vehicles can use the street for access only. Note that weight restrictions on bridges are different - no vehicle may exceed those without special permission.

https://www.irishstatutebook.ie/eli/1997/si/182/made/en/print

"access" means entry or exit by vehicles to or from premises adjacent to or accessible only from a road and includes stopping a vehicle on a roadway solely for the purpose of loading or unloading goods on to or from such vehicle from or to such premises;

This is similar: https://www.google.com/maps/@53.3195901,-6.2788039,3a,43.4y,146.24h,88.39t/data=!3m7!1e1!3m5!1sJ1m6Kb9xFOn1MWNcSgGhsg!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fpanoid%3DJ1m6Kb9xFOn1MWNcSgGhsg%26cb_client%3Dmaps_sv.tactile.gps%26w%3D203%26h%3D100%26yaw%3D177.79732%26pitch%3D0%26thumbfov%3D100!7i16384!8i8192

The objective is to stop people trying to skip the traffic lights and then getting stuck in the lane with opposing traffic.