I've been reading up on the philosopher Hans-Georg Gadamer who said:
"The projecting of the historical horizon, then, is only a phase in the process of understanding, and does not become solidified into the self-alienation of a past consciousness, but is overtaken by our own present horizon of understanding. In the process of understanding there takes place a real fusing of horizons, which means that as the historical horizon is projected, it is simultaneously removed." (Gadamer 1975: 273)
What that means is that as we look back into the past, we shouldn't abandon our current worldview, but try to fuse the ancient paradigm with our own. Cornelius Holtorf's commentary on Gadamer points out, "The horizon includes everything that can be seen from a particular vantage point, and nothing more." So the "historical horizon" must be limited to the particular time and place in which a text was originally produced. It's not possible for the historical interpretation of the Bible to include concepts such as helicopters, the Laws of Thermodynamics, or moral relativism since they did not exist at the time. Not that the Bible can't address those things, but rather that the "historical horizon" can't. We can read the Scriptures in light of new things (but remember Ecclesiastes 1:9!), but can't ignore the original intended meaning. A proper understanding fuses the author's meaning with our current situation(s).
So when, for instance, Jesus says:
And if your hand causes you to sin, cut it off. It is better for you to enter life crippled than with two hands to go to hell, to the unquenchable fire. And if your foot causes you to sin, cut it off. It is better for you to enter life lame than with two feet to be thrown into hell. And if your eye causes you to sin, tear it out. It is better for you to enter the kingdom of God with one eye than with two eyes to be thrown into hell, ‘where their worm does not die and the fire is not quenched.’—Mark 9:43-48 (ESV)
we need to understand what Jesus was communicating to his original disciples. But we also need to reconcile his teachings with our own preconceptions. Some have taken this passage quite seriously and "literally", but in the last two millenia we have few examples of self-mutilation based on this passage. So our instinct is to find an allegorical or symbolic meaning.
One of the hermeneutical challenges for texts, such as the Bible, that have been infused in our Western culture is that over time the historical horizon fades and blurs. We lose track of what the text actually says and substitute some traditional interpretation—almost without knowing what we are doing. For that reason, a great deal of exegesis is devoted to recovering the "original meaning" or intention of the author. Only after that has been accomplished can we propose interpretations informed by modern conceptualizations.
But as Gadamer suggests, that's just one step in the process. The subsequent steps involve integrating the historical meaning into the tradition of interpretation and ultimately into our web of understanding. In that sense, X can mean different, even opposite, things for A and for B. However, there is some hope that we can recover one historical (or original) meaning that is fairly objective.
(As a side note, this site primarily focuses on the defining of the historical horizon, since that's the most objective portion of the process. The next most objective portion is to recover the history of interpretation: how did previous commentators understand the text? The final step, integrating with individual worldviews, is left as an exercise for the reader.)