Why is effective school management important in the classroom?

School management is a big topic because it covers a huge range of subjects.  School management topics include things like attendance, student behavior, dress code, curriculum, enrollment, recruiting, retention, scheduling, hiring, firing, budgeting, pay scales, teacher evaluations, professional development requirements, etc.  
With all of the possible responsibilities for school management, I'm glad that the question specifically asks about school management's impact on daily classroom teaching and learning.  Many of the above items do affect the classroom.  I'd like to expand on three of them. 
Let's start with the hiring of new faculty members.  I have served on several committees that have made the final recommendation to the school board about which teaching candidate to offer a contract to.  A central concern is always "What can this teacher do for us in the classroom?"  Along with that question is the question of teaching experience.  Are we hiring a first year teacher or a master teacher?  A master teacher likely has solid classroom management procedures in place, and that will allow that teacher to effectively focus on student learning rather than student behavior.  A classroom that is focused on student learning is a better classroom.  Effective school management tries to always hire the most effective teacher in order to have effective classrooms. 
Next, let's look at how school management's budgeting can impact classroom learning.  I teach science, and as a consequence, I feel that I am very aware of my budget.  I am currently fortunate enough that I have been able to supply every lab investigation with funding from my school budget.  That directly impacts student learning because labs allow students to collaboratively work in groups, problem solve, and practice content skills.  Those are all linked to student achievement. Without school management recognizing the value in funding school labs and effectively running a budget, science labs in schools would end to the detriment of classroom teachers and student learners.  
Curriculum is next.  Effective school managers are involved with school curriculum.  They need to ensure that the curriculum is in line with government education policies.  Additionally, effective school management regarding curriculum involves making sure that the curriculum is broad and balanced.  The curriculum should also spiral in its scope and sequence across grade levels.   Finally, effective school management will determine what the curriculum review process will entail.  Without these procedures in place, the overall direction of classroom student learning runs the risk of not having enough guidance.  I like the analogy of driving and directions.  Teachers might be great drivers, but without directions, 10 teachers might drive in 10 different directions.  School management gives the directions and the end goals.  Teachers drive students toward that goal.  Effective school management doesn't guarantee effective classrooms, but it does help a lot. 
https://www.edb.gov.hk/attachment/en/sch-admin/sbm/sbm-forms-references/tips%20for%20school%20managers_eng.pdf