Love means that I care about the welfare of the person I love. To the extent that it is genuine, my caring is not a smothering of the person or a possessive clinging. 

参考译文：爱意味着我关心我所爱的人的幸福。只要这种关心是真诚的，那么我的关心就不会是对我爱的人的某种压抑或占有性的依附.

解析：to the extent that sb/sth do sth 达到某人/某事做某事的程度,可以理解为：to+名词+that从句构成的介词短语作条件状语。(that引导同位语从句，用来说明extent的具体内容。）

to the extent that=到何种程度/到那种程度/到…的程度

We may not be able to do it to the extent that we would like.  

我们也许无法把这件事做到我们希望的程度。

He could only be sorry to the extent that this affected his grandchildren.  

这件事甚至都影响到了他的孙辈，他只有伤心的份儿。

I became pregnant but this man was very violent towards me to the extent that I lost our baby.

我怀孕了，但是这个男人对我非常粗暴，致使我流产了。

It has increased to such an extent that Ghana can now export maize.

玉米产量增长得如此迅速，现在加纳已经可以出口玉米了。