LTE is short for Long Term Evolution, a wireless data implementation marketed as LTE-4G. Simply put, it is a faster implementation compared to 3G or WCDMA.
First you need to have a phone that is LTE capable in order to access LTE. (ipone 5, Galaxy S4, z10, HTC One, Lumia 820, etc)
Second is you need to have an LTE capable sim. You may ask Globe to change your sim if you'd want to access LTE assuming you have an LTE capable device.
To know that you have are connected to an LTE network, the word LTE or an LTE logo beside the signal bars would appear.
Please note that Globe's LTE network is still limited as of the moment and only a few areas are covered.
For more you can check http://network.globe.com.ph/fourG/index